Question

A coil 3.60 cm radius, containing 600 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 3.35×10−5 T/s4 )t4. The coil is connected to a 660-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.Find the magnitude of the induced emf in the coil as a function of time.

Answer 1

the emf will be
`2.4(1.20* 10^(-2)+13.4* 10^(-5)t^3)`

Step-by-step explanation:

We have given radius of the coil r = 3.6 cm = 0.036 m

So area
`A=\pi r^2=3.14* 0.036^2=0.0040m^2`

Number of turns N = 600

Emf is given by
`e=N(d\Phi )/(dt)`

`e=N(d\Phi )/(dt)=NA(dB)/(dt)=600* 0.0040* d(1.20* 10^(-2)t+3.35* 10^(-5)t^4)/(dt)=2.4(1.20* 10^(-2)+13.4* 10^(-5)t^3)`

So the emf will be
`2.4(1.20* 10^(-2)+13.4* 10^(-5)t^3)`